116 LearnersLast updated on May 29th, 2025
Square of 313
The product of multiplying an integer by itself is the square of a number. The square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 313.
What is the Square of 313
The square of a number is the product of the number and itself.
The square of 313 is 313 × 313.
The square of a number often ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 313², where 313 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive. For example, 5² = 25; -5² = 25.
The square of 313 is 313 × 313 = 97969.
Square of 313 in exponential form: 313²
Square of 313 in arithmetic form: 313 × 313
How to Calculate the Value of Square of 313
The square of a number is found by multiplying the number by itself. Let’s learn how to find the square of a number. These are the common methods used to find the square of a number.
- By Multiplication Method
- Using a Formula (a2)
- Using a Calculator
By the Multiplication Method
In this method, we multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 313.
Step 1: Identify the number. Here, the number is 313.
Step 2: Multiplying the number by itself, we get, 313 × 313 = 97969.
The square of 313 is 97969.
Using a Formula (a²)
In this method, the formula a² is used to find the square of the number, where a is the number.
Step 1: Understanding the equation Square of a number = a²
a² = a × a
Step 2: Identifying the number and substituting the value in the equation.
Here, ‘a’ is 313.
So: 313² = 313 × 313 = 97969
By Using a Calculator
Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 313.
Step 1: Enter the number in the calculator. Enter 313 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 313 × 313.
Step 3: Press the equal button to find the answer. Here, the square of 313 is 97969.
Tips and Tricks for the Square of 313
Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.
- The square of an even number is always an even number. For example, 6² = 36.
- The square of an odd number is always an odd number. For example, 5² = 25.
- The last digit of the square of a number is often 0, 1, 4, 5, 6, or 9.
- If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
Common Mistakes to Avoid When Calculating the Square of 313
Mistakes are common among kids when doing math, especially when finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.
Mistake 1
Calculation errors
Calculation errors mostly happen when students skip steps or swap the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found.
For example, the square of 25 is 625, and the square root of 625 is ±25.
Solved Examples on Square of 313
Problem 1
A rectangular garden has a length of 313 meters and a width of 200 meters. Find its area.
The area of a rectangle = length × width
Area = 313 m × 200 m = 62600 m²
Explanation
The area of the rectangular garden is 62600 m². This is calculated by multiplying the length by the width.
Problem 2
Maya wants to cover her square floor, which has a side length of 313 feet, with tiles. If each tile costs $5, how much will it cost to cover the entire floor?
The length of the floor = 313 feet
Cost to cover 1 square foot = $5
To find the total cost, we find the area of the floor: Area of the floor = a²
Here, a = 313
Therefore, the area = 313² = 313 × 313 = 97969.
The cost to cover the floor = 97969 × 5 = 489845.
The total cost = $489845
Explanation
To find the cost to cover the floor, we multiply the area of the floor by the cost to cover per square foot. So, the total cost is $489845.
Problem 3
Find the area of a circle whose radius is 313 meters.
The area of the circle = 307,995.46 m²
Explanation
The area of a circle = πr²
Here, r = 313
Therefore, the area of the circle = π × 313² ≈ 3.14 × 313 × 313 = 307995.46 m².
Problem 4
The area of the square is 97969 cm². Find the perimeter of the square.
The perimeter of the square is 1252 cm
Explanation
The area of the square = a²
Here, the area is 97969 cm²
The length of the side is √97969 = 313
Perimeter of the square = 4a
Here, a = 313
Therefore, the perimeter = 4 × 313 = 1252 cm.
Problem 5
Find the square of 314.
The square of 314 is 98596
Explanation
The square of 314 is found by multiplying 314 by 314.
So, the square = 314 × 314 = 98596
FAQs on Square of 313
1.What is the square of 313?
2.What is the square root of 313?
3.Is 313 a prime number?
4.What are the first few multiples of 313?
5.What is the square of 312?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square of 313?
8.How do technology and digital tools in United States support learning Algebra and Square of 313?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square 313
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 313.
- Exponential form: A mathematical expression where a number is raised to a power. For example, 9² where 9 is the base and 2 is the exponent.
- Square root: The operation that finds a number whose square is the given number. For example, the square root of 49 is 7.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6².
- Rectangle: A quadrilateral with opposite sides equal and four right angles, used here in calculating area.
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
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